Approximation of Uniform Transport Process on a Finite Interval to Brownian Motion

Abstract

Let us consider a finite closed interval [− a, a] which will be thought of as being a medium capable of transporting particles. These particles may move only to the right or to the left with the constant speed c, and each particle changes the moving-direction during the time Δ with probability kΔ + o(Δ). If a right- (left-) moving particle hits the boundary point a (— a), then either it turns to the left (right) with probability 1 — q1(1 − q-1) or dies with probability q1(q-1).